m -1 m -1 a -2 b -2 cwhere -1 and -2 indicate, respectively, that the first and second argument will follow. This notation is very flexible - in fact, it is too flexible, because it also allows us to write things like
m -1 a -2 m -l b -2 c
m -2 m -1 b -1 c -1 awhich, though each has the same meanings as the second expression above, are even more confusing.
m -2 m -2 c -1 b -1 a
The usual algebraic notation for the associative law, using * instead of m for multiplication, is
(a * b) * c = a * (b * c) .Another common algebraic notation is the so called Polish prefix form, in which the associative law for * would be written as
* * a b c = * a * b c .And here are the parse tree forms for the two expressions, again using * instead of m:
* * / \ / \ * c a * / \ / \ a b b cExercise: Say what's good and bad about each of these 4 notations, and why.